When installing Ubuntu, I made the partition really small. I would like to know if applications like vlc or Clementine be installed and run from the cloud?
You may run a full Ubuntu desktop in the cloud, however multimedia apps will suffer because of network latency and throughput
I have been able to run some applications from a dropbox share before (I can't see why you couldn't do the same with UbuntuOne). I did this for an experiment but it did work, albeit slow!
For example, if you have your dropbox share linked to ~/dropbox and you wanted to free up space, you could do this by moving your main vlc /usr/share/vlc directory to you dropbox and create a symbolic link back to your /usr/share directory.
But at the end of the day, I think this isn't a great solution and you would probably be far better off running some of the apps off a usb stick if storage is an issue.